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Kolmogorov forward differential equation

  • Thread starter Little Miss Actuary
  • Start date
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Little Miss Actuary

Member
I'm sure this is a really simple question... please can someone explain when you should use the version of Kolmogorov forward differential equation given on page 33 of the formula book and when you should use the one on page 38? :confused: I'm sure I am missing something so obvious :eek:

I think my main problem is that I don't understand the difference between

(tpx)^(gh)
and
pgh(x,x+t)

Eek :eek: I tried my best with the formatting. By ^ I don't mean to the power of, I just mean superscript, above the subscript x.

Please can some lovely person explain :D Thanks.
 
it's been a while since i studied that, but i think those two formulas both give the probability you are in state g at time x, and state h at time x+t (allowing for the possibility of jumping somewhere else in between).

so both formulas should be equivalent...
 
AFAIK, they're the same formula but using different notation. The first one uses the notation from the general stochastic model in chapter 5, the second one uses the Markov notation in chapter 6. If you know how to interpret and apply them, it doesn't matter which you use.
 
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